Finite Group Databasebeta

← #14721520

Subgroups — #14721520

Order 2816.

1202 conjugacy classes of subgroups; only the 395 normal subgroups are shown.

normal subgroups only

This group has 1202 conjugacy classes of subgroups — too many to draw. Only its 395 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077697C211yesmaximal, characteristic, complemented
2#13071537C211yesmaximal, characteristic, complemented
3#13067176C216yesmaximal, complemented
4#13067111C216yesmaximal, complemented
5C11×#3497C211yesmaximal, characteristic
6C2×C11×2−1+4—21no—
7C11×#550C414yescomplemented
8D4×Q8×C11C414yescomplemented
9C11×#548—24no—
10C11×#537—23no—
11C11×#532C2216yes—
12C2×C4×Q8×C11C2211yescharacteristic
13C2×Q8×Dic11—21no—
14Q8×C11⋊C8—24no—
15#10622598—23no—
16#10622549C2213yes—
17C4×C4⋊Dic11C2213yes—
18#10622538C2216yes—
19#10622175C2214yes—
20#10622175C22112yes—
21C11×2−1+4—44no—
22C11×2−1+4—44no—
23C2×C11×#41—24no—
24C2×C11×#41—26no—
25C22×Q8×C11—24no—
26C22×Q8×C11D411yescharacteristic
27C11×C4⋊Q8C2×C416yes—
28C11×#127C2×C416yes—
29C11×#124—26no—
30C11×C22⋊Q8—212no—
31C11×#121—26no—
32C11×#121—212no—
33C11×#121C2314yes—
34C4×Q8×C11C2×C414yes—
35C4×Q8×C11D414yes—
36C4×D4×C11—26no—
37C4×D4×C11C2×C4112yes—
38C2×C11×C4⋊C4D413yes—
39C2×C42×C11C2313yes—
40Q8×Dic11—44no—
41C2×C4⋊Dic11—23no—
42C2×C4⋊Dic11—23no—
43C2×C4×Dic11—23no—
44C11⋊#95—23no—
45C11⋊#95C2311yescharacteristic
46C11⋊#95C2313yes—
47C22⋊(C11⋊C8)C2314yes—
48C4⋊(C11⋊C8)—26no—
49C4×C11⋊C8—26no—
50#17618—111nomaximal, Sylow
51C11×#41—416no—
52C11×#41—412no—
53C11×#41—412no—
54C2×Q8×C11—26no—
55C2×Q8×C11—416no—
56C2×Q8×C11C22⋊C414yes—
57C2×Q8×C11D814yes—
58C2×Q8×C11SD1614yes—
59C2×D4×C11—24no—
60C2×D4×C11—26no—
61C2×D4×C11—26no—
62C2×D4×C11C22×C414yes—
63C22×C4×C11—212no—
64C22×C4×C11C2×D413yes—
65C22×C4×C11C2×D413yes—
66C22×C4×C11C2411yescharacteristic
67C22×Dic11—21no—
68C22×Dic11—23no—
69C11×C4⋊C4—26no—
70C11×C4⋊C4C22⋊C4112yes—
71C11×C4⋊C4C22×C414yes—
72C11×C22⋊C4—212no—
73C11×C22⋊C4—24no—
74C42×C11C22×C416yes—
75C42×C11C2×D416yes—
76C4⋊Dic11—46no—
77C4⋊Dic11—46no—
78C4×Dic11—46no—
79C2×C11⋊C8—24no—
80#3497D1111yescharacteristic
81#2982—111no—
82#2351—111no—
83#1517—116no—
84#1502—116no—
85C23×C11—24no—
86C23×C11C22×D411yescharacteristic
87Q8×C11—412no—
88Q8×C11#102116yes—
89D4×C11—44no—
90D4×C11—44no—
91D4×C11—44no—
92D4×C11—412no—
93D4×C11—86no—
94C2×C4×C11—24no—
95C2×C4×C11—43no—
96C2×C4×C11—41no—
97C2×C4×C11—424no—
98C2×C4×C11C2×C22⋊C416yes—
99C2×C4×C11C2×C22⋊C416yes—
100C2×C4×C11C2×D816yes—
101C2×C4×C11C2×SD1616yes—
102C2×C4×C11C23×C411yescharacteristic
103C2×C4×C11C22×D411yescharacteristic
104C2×Dic11—22no—
105C2×Dic11—41no—
106C2×Dic11—41no—
107C2×Dic11—43no—
108C2×Dic11—43no—
109C2×Dic11—43no—
110C11⋊C8—44no—
111C2×2−1+4—21no—
112#550Dic1114yescomplemented
113D4×Q8Dic1114yescomplemented
114#548—24no—
115#537—23no—
116#532C2×D1116yes—
117C2×C4×Q8—221no—
118C2×C4×Q8C2×D1111yescharacteristic
119C8×Q8—224no—
120#431—116no—
121#389—223no—
122#382—113no—
123C4×C4⋊C4—113no—
124#327—114no—
125#327—1112no—
126C22×C11—21no—
127C22×C11—21no—
128C22×C11—44no—
129C22×C11—44no—
130C22×C11—44no—
131C22×C11C22×C22⋊C411yescharacteristic
132C22×C11C22×D811yescharacteristic
133C22×C11C22×SD1611yescharacteristic
134C4×C11—21no—
135C4×C11—21no—
136C4×C11—26no—
137C4×C11—44no—
138C4×C11C2×#102112yes—
139Dic11—42no—
140Dic11—83no—
1412−1+4—44no—
1422−1+4—44no—
143C2×#41—24no—
144C2×#41—26no—
145C22×Q8—24no—
146C22×Q8C22⋊D1111yescharacteristic
147C4⋊Q8C2×Dic1116yes—
148#127C2×Dic1116yes—
149#124—26no—
150C22⋊Q8—212no—
151#121—26no—
152#121—212no—
153#121C22×D1114yes—
154C4×Q8—444no—
155C4×Q8C2×Dic1114yes—
156C4×Q8C22⋊D1114yes—
157C4×D4—26no—
158C4×D4C2×Dic11112yes—
159C2×C4⋊C4—223no—
160C2×C4⋊C4—223no—
161C2×C4⋊C4C22⋊D1113yes—
162C2×C42—223no—
163C2×C42C22×D1113yes—
164C4⋊C8—226no—
165C22⋊C8—114no—
166C4×C8—226no—
167#95—111no—
168#95—113no—
169#95—223no—
170C2×C11—21no—
171C2×C11—21no—
172C2×C11—84no—
173C2×C11#288411yescharacteristic
174C2×C11C22×#10211yescharacteristic
175C2×C11#290111yescharacteristic
176#41—416no—
177#41—412no—
178#41—412no—
179C2×Q8—26no—
180C2×Q8—416no—
181C2×Q8#432314yes—
182C2×Q8#432414yes—
183C2×Q8C22⋊Dic1114yes—
184C2×D4—24no—
185C2×D4—26no—
186C2×D4—26no—
187C2×D4C22×Dic1114yes—
188C22×C4—212no—
189C22×C4—221no—
190C22×C4—223no—
191C22×C4C2×C22⋊D1113yes—
192C22×C4C2×C22⋊D1113yes—
193C22×C4C23×D1111yescharacteristic
194C2×C8—224no—
195C4⋊C4—26no—
196C4⋊C4—446no—
197C4⋊C4—446no—
198C4⋊C4C22⋊Dic11112yes—
199C4⋊C4C22×Dic1114yes—
200C22⋊C4—212no—
201C22⋊C4—24no—
202C42—446no—
203C42C22×Dic1116yes—
204C42C2×C22⋊D1116yes—
205C11#1761811yescharacteristic, complemented, Sylow
206C23—24no—
207C23C22×C22⋊D1111yescharacteristic
208Q8—412no—
209Q8#66896116yes—
210D4—44no—
211D4—44no—
212D4—44no—
213D4—412no—
214D4—86no—
215C2×C4—24no—
216C2×C4—43no—
217C2×C4—41no—
218C2×C4—424no—
219C2×C4—222no—
220C2×C4—441no—
221C2×C4—441no—
222C2×C4—443no—
223C2×C4—443no—
224C2×C4—443no—
225C2×C4C2×#432316yes—
226C2×C4C2×#432416yes—
227C2×C4C2×C22⋊Dic1116yes—
228C2×C4C2×C22⋊Dic1116yes—
229C2×C4C23×Dic1111yescharacteristic
230C2×C4C22×C22⋊D1111yescharacteristic
231C8—444no—
232C22—21no—
233C22—21no—
234C22—44no—
235C22—44no—
236C22—44no—
237C22C22×#432311yescharacteristic
238C22C22×#432411yescharacteristic
239C22C22×C22⋊Dic1111yescharacteristic
240C4—21no—
241C4—21no—
242C4—26no—
243C4—44no—
244C4—442no—
245C4—883no—
246C4C2×#66896112yes—
247C2—21no—
248C2—21no—
249C2—84no—
250C2#1307708011yescharacteristic
251C2C22×#6689611yescharacteristic
252C2#1307716311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3497C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenter#3497D11
hypocenterC11#17618
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ #3497

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13077697C2semidirect
2. #13071537C2semidirect
3. #13067176C2semidirect
4. #13067111C2semidirect
7. C11×#550C4semidirect
8. D4×Q8×C11C4semidirect
112. #550Dic11semidirect
113. D4×Q8Dic11semidirect
205. C11#17618semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130776972
#130715372
#130671762
#130671112
C11×#34972
#1761811